A Lecture on the S-Procedure

摘要: The purpose of this lecture is to give an introduction the S-procedure and its use in systems control applications. notion was coined by researches former Soviet union who used it stability analysis nonlinear systems. Several important results analysis, such as circle criterion, Popov Kalman-YakubovichPopov Lemma, are closely related S-procedure. really nothing but a Lagrange relaxation technique, which mostly has been problems with quadratic constraints. One main that will be presented note condition for exactness (losslessness) relaxation. few known, yet extremely important, cases when lossless there one objective subject constraint. We derive criterion. useful also not exact (lossy). reason can obtain sufficient conditions terms Linear Matrix Inequalities (LMI) large number nonconvex analysis. It numerous applications uncertain differential equations.